Clemson University TigerPrints All Theses Theses 5-2007 MINIMUM SAMPLE SIZE NEEDED TO CONSTRUCT CUSHION CURVES BASED ON THE STRESS-ENERGY METHOD Patricia Marcondes Clemson University, [email protected] Follow this and additional works at: https://tigerprints.clemson.edu/all_theses Part of the Engineering Commons Recommended Citation Marcondes, Patricia, "MINIMUM SAMPLE SIZE NEEDED TO CONSTRUCT CUSHION CURVES BASED ON THE STRESS- ENERGY METHOD" (2007). All Theses. 135. https://tigerprints.clemson.edu/all_theses/135 This Thesis is brought to you for free and open access by the Theses at TigerPrints. It has been accepted for inclusion in All Theses by an authorized administrator of TigerPrints. For more information, please contact [email protected]. MINIMUM SAMPLE SIZE NEEDED TO CONSTRUCT CUSHION CURVES BASED ON THE STRESS-ENERGY METHOD A Thesis Presented to the Graduate School of Clemson University In Partial Fulfillment of the Requirements for the Degree Master of Science Packaging Science by Patricia Dione Guerra Marcondes May 2007 Accepted by: Dr. Duncan O. Darby, Committee Chair Mr. Gregory S. Batt Dr. Hoke S. Hill, Jr. Dr. Matthew Daum ABSTRACT Cushion curves are graphical tools used by protective package designers to evaluate and choose foamed cushioning materials. Thousands of samples and hundreds of laboratory hours are needed to produce a full set of cushion curves according to the ASTM procedure D 1596. The stress-energy method considerably reduces the number of samples needed to construct cushion curves for closed-cell cushioning materials. Consequently the laboratory and data analysis time are reduced as well. The stress-energy method was used to find the minimum sample size needed to construct cushion curves for closed-cell cushioning materials. A reference set of data collected for ARCEL Resin® foam blocks using the stress-energy method was used. Lines fitted to this reference data set were statistically compared against lines fitted to reduced size sample sets. This comparison revealed that 15 samples (5 replicates at 3 energy levels) were sufficient to fit lines without statistical difference. The data analysis also showed a limitation of the stress-energy method associated with densities higher than 2.2 lb/ft3 for the materials used. Cushion curves for two densities of expanded polyethylene were successfully constructed using the reduced sample size of 15. These curves were compared to published data for EPE and were found to vary within expected lab-to-lab tolerances. iii iv DEDICATION This work is dedicated to the memory of my loving husband, Dr. Jorge Aparecido Marcondes. v vi ACKNOWLEDGMENTS This work would not have been possible without the support of Nova Chemicals, Inc. who allowed me to use their materials and data for this research. I would also like to recognize Span America of Greenville, South Carolina for donating the expanded polyethylene foam used in this research. I would like to thank my advisor, Dr. Duncan Darby for his guidance throughout the process leading up to this publication. His thoughtful input and support got me throughout the difficult writing process. His love of learning and teaching were truly inspiring. I must also express my gratitude to the other members of my committee, Greg Batt, Hoke Hill, and Matthew Daum for their guidance and support. I would like to thank Greg Batt for thinking of me for the ARCEL Resin® project. If it weren’t for that, this work would not have happened. Thanks to Dr. Matthew Daum’s practical insight, a thesis was born from the ARCEL® project. Mr. Herb Schueneman and William Kipp also contributed by reading sections of the manuscript and offering their expert opinion. Finally, without the support of my friends in Clemson I could not have dedicated the time to complete this degree. vii viii TABLE OF CONTENTS Page TITLE PAGE .................................................................................................................... i ABSTRACT........................................................................................................................ iii DEDICATION ................................................................................................................. iv ACKNOWLEDGEMENTS ........................................................................................... vii LIST OF TABLES ............................................................................................................ xi LIST OF FIGURES.......................................................................................................... xiii CHAPTER 1. INTRODUCTION.......................................................................................... 1 2. REVIEW OF LITERATURE........................................................................ 5 Concepts in Cushioning Material Deflection............................................................................................. 6 Cushioning Material Classification .......................................................... 7 Mechanical Shock....................................................................................... 9 Conventional Evaluation of Cushioning Materials for Protective Applications............................................... 11 Evaluation of Cushioning Materials Using Stress-Energy Relationship..................................................... 13 Evaluation of Sample Statistics for Statistical Difference ........................................................................... 17 3. MATERIALS AND METHODS.................................................................. 19 Test Equipment................................................................................................. 19 Testing Phases ............................................................................................ 24 Phase I – ARCEL Resin ® Data Collection ................................... 25 Phase II – Statistical Evaluation of Lines Fit to Reduced Sample................................................................. 27 Phase III – Reduced Sample Evaluation Using EPE..................................................................................... 28 Phase IV - Homogeneity Testing of Individual Impact Data ............................................................... 30 ix Table of Contents (Continued) Page 4. RESULTS AND CONCLUSIONS .............................................................. 31 Phase I ......................................................................................................... 31 Phase II........................................................................................................ 35 Linearization......................................................................................... 35 Two-point Reduction.......................................................................... 39 Three-point Reduction ....................................................................... 40 Phase III – Test of Three-point Plan Using EPE............................................................................................ 43 Phase IV – Homogeneity Testing of Individual Impact Data....................................................................... 47 Summary of Conclusions.......................................................................... 48 5. RECOMMENDATIONS............................................................................... 51 APPENDICES................................................................................................................... 53 A: ARCEL Resin ® Test Template.............................................................. 55 B: Expanded Polyethylene Test Template ................................................. 59 REFERENCES.................................................................................................................. 63 x LIST OF TABLES Table Page 1. Summary of materials tested...................................................................................... 26 2. Summary of reference data ........................................................................................ 39 3. Results of statistical comparison for lines with two energy levels........................................................................................................... 39 4. Results of statistical comparison for lines with three energy levels (H=0.05) ................................................................................ 41 5. Energy values for 3-point test of Ethafoam™ ....................................................... 43 6. Predicted G using 3-point equation vs. ETHACALC® or 1ST Impact on 2-in Ethafoam™.................................................................................................... 44 7. Predicted G using 3-point equation vs. ETHACALC® for averaged 2nd -5th impacts on 2-in Ethafoam™ ...................................................................................... 45 8. Homogeneity testing results of individual drops on ARCEL® Resin blocks........................................................................................ 47 xi xii LIST OF FIGURES Figure Page 1. Open cell and closed-cell foams................................................................................ 8 2. Simplified shock pulse ................................................................................................ 10 3. Example of pair of cushion curves........................................................................... 12 4. Illustration